Focused short-pulsed laser beams are used for cutting and modifying transparent substrates, such as glass, through the process of nonlinear absorption via multi-photon ionization and subsequent ablation. Such laser systems must thus deliver a very small spot size and have high repetition rates in order to process materials at significant speeds. Typically laser processing has used Gaussian laser beams. The tight focus of a laser beam with a Gaussian intensity profile has a Rayleigh range ZR given by:
                              Z          R                =                              π            ⁢                                                  ⁢                          n              o                        ⁢                          w              o              2                                            λ            o                                              (        1        )            
The Rayleigh range represents the distance over which the spot size wo of the beam will increase by √{square root over (2)} in a material of refractive index no at wavelength λ0. This limitation is imposed by diffraction. As shown in Eqn. 1 above, the Rayleigh range is related directly to the spot size, thus a tight focus (i.e. small spot size) cannot have a long Rayleigh range. Thus, the small spot size is maintained for an unsuitably short distance. If such a beam is used to drill through a material by changing the depth of the focal region, the rapid expansion of the spot on either side of the focus will require a large region free of optical distortion that might limit the focus properties of the beam. Such a short Rayleigh range also requires multiple pulses to cut through a thick sample.
Another approach to maintaining a tightly focused beam in a material is to use nonlinear filamentation via the Kerr effect, which yields a self-focusing phenomenon. In this process, the nonlinear Kerr effect causes the index at the center of the beam to increase, thereby creating a waveguide that counteracts the diffraction effect described above. The beam size can be maintained over a much longer length than that given in Eq. 1 above and is no longer susceptible to surface phase distortions because the focus is defined at the surface. To produce a sufficient Kerr effect, the power of the incident laser beam must exceed a critical value given by equation 2 below:
                              P          Cr                =                              3.72            ⁢                                                  ⁢                          λ              o              2                                            8            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          n              o                        ⁢                          n              2                                                          (        2        )            where n2 is the second-order nonlinear refractive index.
Despite the benefit of this extended focal range, generating beams in accordance with the Kerr effect undesirably requires much more power than the above described Gaussian beam approach.
Accordingly, there is a continual need for a beam generation method in a laser cutting system which achieves a beam(s) having a controlled spot size, longer focal length, while minimizing power requirements and increasing process speed.